* to strong rotation and elongation of the fluid @cite Blais2013.
*
* The stream function $\Psi$ of this Rayleigh-Kothe vortex is defined as:
-@f[
-\Psi = \frac{1}{\pi} \sin^2 (\pi x) \sin^2 (\pi y) \cos \left( \pi \frac{t}{T}
-\right)
-@f]
+ * @f[
+ * \Psi = \frac{1}{\pi} \sin^2 (\pi x) \sin^2 (\pi y) \cos \left( \pi
+ * \frac{t}{T} \right)
+ * @f]
* where $T$ is half the period of the flow. The velocity profile in 2D
-($\textbf{u}=[u,v]^T$) is :
-@f{eqnarray*}{
- u &=& - \frac{\partial\Psi}{\partial y} = -2 \sin^2 (\pi x) \sin (\pi y)
-\cos (\pi y) \cos \left( \pi \frac{t}{T} \right)\\ v &=&
-\frac{\partial\Psi}{\partial x} = 2 \cos(\pi x) \sin(\pi x) \sin^2 (\pi y) \cos
-\left( \pi \frac{t}{T} \right)
-@f}
+ * ($\textbf{u}=[u,v]^T$) is:
+ * @f{eqnarray*}{
+ * u &=& - \frac{\partial\Psi}{\partial y} = -2 \sin^2 (\pi x) \sin (\pi y)
+ * \cos (\pi y) \cos \left( \pi \frac{t}{T} \right)\\ v &=&
+ * \frac{\partial\Psi}{\partial x} = 2 \cos(\pi x) \sin(\pi x) \sin^2 (\pi y)
+ * \cos \left( \pi \frac{t}{T} \right)
+ * @f}
* where $T$ is half the period of the flow.
*
* The velocity profile is illustrated in the following animation:
*
-@htmlonly
-<p align="center">
- <iframe width="560" height="500"
-src="https://www.youtube.com/embed/m6hQm7etji8" frameborder="0"
- allow="accelerometer; autoplay; encrypted-media; gyroscope;
-picture-in-picture" allowfullscreen></iframe>
- </p>
-@endhtmlonly
+ * @htmlonly
+ * <p align="center">
+ * <iframe width="560" height="500"
+ * src="https://www.youtube.com/embed/m6hQm7etji8" frameborder="0"
+ * allow="accelerometer; autoplay; encrypted-media; gyroscope;
+ * picture-in-picture" allowfullscreen></iframe>
+ * </p>
+ * @endhtmlonly
*
* It can be seen that this velocity reverses periodically due to the term
* $\cos \left( \pi \frac{t}{T} \right)$ and that material will end up at its
* <code>FE_Hermite<3>(3)</code>:
*
* @verbatim
- * (40,41,44,45)__(42,43,46,47) (40,41,44,45)__(42,43,46,47)
- * (56,57,60,61) (58,59,62,63) (56,57,60,61) (58,59,62,63)
- * / | | / / |
- * / | | / / |
- * / | | / / |
- *(32,33,36,37)| | (32,33,36,37)__(34,35,38,39)
- *(48,49,52,53)| | (48,49,52,53) (50,51,54,55)
- * | | | | | |
- * |( 8,9,12,13 )__(10,11,14,15) | |(10,11,14,15)
- * |(24,25,28,29) (26,27,30,31) | |(26,27,30,31)
- * | / / | | /
- * | / / | | /
- * | / / | | /
- * ( 0,1,4,5 )___( 2,3,6,7 ) ( 0,1,4,5 )___( 2,3,6,7 )
- * (16,17,20,21) (18,19,22,23) (16,17,20,21) (18,19,22,23)
+ * (40,41,44,45)__(42,43,46,47) (40,41,44,45)__(42,43,46,47)
+ * (56,57,60,61) (58,59,62,63) (56,57,60,61) (58,59,62,63)
+ * / | | / / |
+ * / | | / / |
+ * / | | / / |
+ * (32,33,36,37)| | (32,33,36,37)__(34,35,38,39)
+ * (48,49,52,53)| | (48,49,52,53) (50,51,54,55)
+ * | | | | | |
+ * |( 8,9,12,13 )__(10,11,14,15) | |(10,11,14,15)
+ * |(24,25,28,29) (26,27,30,31) | |(26,27,30,31)
+ * | / / | | /
+ * | / / | | /
+ * | / / | | /
+ * ( 0,1,4,5 )___( 2,3,6,7 ) ( 0,1,4,5 )___( 2,3,6,7 )
+ * (16,17,20,21) (18,19,22,23) (16,17,20,21) (18,19,22,23)
* @endverbatim
*
* Due to the increased regularity constraints many of these functions are